Converting Nominal Interest Rates to Different Compounding Periods

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Sometimes the compounding period of the interest on a loan will not match the when deposits are expected to be made. For example, you are expected to make monthly mortgage payments, but the interest is compounded semi-annually. In cases like these, we must convert the nominal rate to an equivalent rate that matches the timing of the cash flows.

Q1. Find the equivalent rate of interest for a loan rated at 8% compounded semi-annually to interest compounded annually.

Note: When finding the equivalent annual rate, it is called the effective annual rate.

Q2. Find the equivalent rate of interest for a loan rated at 3.5% compounded monthly to interest compounded semi-annually.

[pearlolatunde]

Thank you so much❤❤❤❤

This was very helpful

[jeremienz]

how can we have a monthly compound interest 3, 5% and 6 months later( semi-annually) and having again the semi-annual interest close to 3.5%. if we want to have an idea about the range where our i' will be located, we can sum up the monthly interest, so (3.5+3.5+3.5+3.5+3.5+3.5)= 21% so our interest should not be less than 21% after 6 months. how can you explain that?

[eekanspok-oqxm]

Could you please help me with this one?

Three banks X, Y and Z, each offers a different effective interest rate on its saving account.
(Hint: Assume 1 year to be 366 days).
Bank Nominal Interest Rate Compounding Period
X 8.25% compounded daily
Y 8.25% compounded Monthly
Z 8.30% compounded Quarterly